{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "## 5.3 总结与计算描述性的统计信息 Summarizing and Computing Descriptive Statistics"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "source": [
    "# 模块导入\r\n",
    "import os, sys\r\n",
    "sys.path.append(os.path.dirname(os.getcwd()))\r\n",
    "import numpy\r\n",
    "import pandas\r\n",
    "import matplotlib.pyplot\r\n",
    "from dependency import arr_info"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "### 绪  论\r\n",
    "\r\n",
    "约简计算（reduction statistics）与汇总计算（summary statistics）\r\n",
    "\r\n",
    "约简型（reduction）：\r\n",
    "+ `object.count()`：统计所有非 `NaN` 的个数\r\n",
    "+ `object.sum()`：求和\r\n",
    "+ `object.mean()`：平均值\r\n",
    "+ `object.std()`：标准差，自由度默认为 (n-1)，即 `ddof=1`；\r\n",
    "+ `object.var()`：方差，自由度默认为 (n-1)，即 `ddof=1`；\r\n",
    "+ `object.max()`，`array.min()`：最大值，最小值；\r\n",
    "+ `object.idxmax()`、`object.idxmin()`：间接统计，返回最大值、最小值的轴索引；\r\n",
    "+ 【已弃用】`object.argmax()`、`object.argmin()`：间接统计，返回最大值、最小值的轴索引；\r\n",
    "+ `object.median()`：样本中位数\r\n",
    "+ `object.mad()`：根据平均值计算平均绝对离差\r\n",
    "+ `object.quantile(q=)`：计算样本的分位数（0到1），参数 `q=` 设置百分比，默认为0.5；\r\n",
    "+ `object.skew()`：样本值的偏度，即：三阶矩\r\n",
    "+ `object.sum()`：样本值的峰度，即：四阶矩\r\n",
    "\r\n",
    "累计型（accumulation）：\r\n",
    "+ `object.cumsum()`：所有元素的累计和\r\n",
    "+ `object.cumprod()`：所有元素的累计积\r\n",
    "+ `object.cummax()`、`object.cummin()`：样本值的累计最大值、累计最小值\r\n",
    "+ `object.diff()`：计算一阶差分（对时间序列很有用）\r\n",
    "+ `object.pct_change()`：计算百分数变化\r\n",
    "\r\n",
    "特殊：既不是约简型，也不是累计型\r\n",
    "+ `object.describe()`\r\n",
    "\r\n",
    "约简计算的类方法通常有以下参数：\r\n",
    "\r\n",
    "+ `axis=`：约简计算的轴，对于DataFrame：`axis=0` 时计算每列的值（默认），`axis=1` 时计算每行的值；\r\n",
    "+ `skipna=`：排除缺失值（默认为True）；\r\n",
    "+ `level=`：如果是层次化索引（MultiIndex），则根据level分组约简；\r\n",
    "\r\n",
    "注意：与NumPy不同，pandas没有上述类方法所对应的函数"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "# 约简型统计方法\r\n",
    "\r\n",
    "frame0_1 = pandas.DataFrame([[1.4, numpy.NaN], [7.1, -4.5],[numpy.NaN, numpy.NaN], [0.75, -1.3]], columns=[\"A\", \"B\"])\r\n",
    "arr_info([ frame0_1 ])\r\n",
    "\r\n",
    "## axis参数\r\n",
    "arr_info([ frame0_1.sum() ])\r\n",
    "arr_info([ frame0_1.sum(axis=1) ])"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "## skipna参数\r\n",
    "arr_info([ frame0_1.mean(axis=1) ])     # 默认跳过NaN，除非整行、列都是NaN\r\n",
    "arr_info([ frame0_1.mean(axis=1, skipna=False) ])\r\n",
    "arr_info([ frame0_1.std() ])    # 注意：pandas默认计算修正样本标准差，与NumPy相反！"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "## 间接统计：返回索引值\r\n",
    "arr_info([ frame0_1.idxmax() ])\r\n",
    "arr_info([ frame0_1.idxmin() ])\r\n",
    "arr_info([ frame0_1.quantile(q=0.95) ])"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "# 累计型统计方法\r\n",
    "arr_info([ frame0_1.cumsum() ])     # 累加\r\n",
    "arr_info([ frame0_1.cumprod() ])    # 累乘\r\n",
    "arr_info([ frame0_1.diff() ])       # 一阶差分\r\n",
    "arr_info([ frame0_1.pct_change() ])    # 百分数变化"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "# 特例：既不是约简型，也不是累计型————统计信息汇总\r\n",
    "ser0_1 = pandas.Series([\"a\", \"c\", \"a\", \"b\"] * 4)\r\n",
    "\r\n",
    "arr_info([ frame0_1.describe() ])\r\n",
    "\r\n",
    "arr_info([ ser0_1 ])\r\n",
    "arr_info([ ser0_1.describe() ])     # 对于非数值数据（non-numeric data），返回的统计汇总有所不同"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "### 5.3.1 相关系数与协方差 Correlation and Covariance\r\n",
    "\r\n",
    "部分统计方法是通过参数对（pairs of arguments）计算得出的\r\n",
    "\r\n",
    "计算协方差（矩阵）：\r\n",
    "+ `object.cov()`：计算pandas.Series或pandas.DataFrame的协方差；\r\n",
    "+ `numpy.cov(data, rowvar=True, ddof=1)`：data可以是numpy.ndarray，也可以是pandas.Series、pandas.DataFrame；默认每行为一个统计学中的随机变量，而rowvar参数设置为False，则按每列为一个随机变量来处理\r\n",
    "\r\n",
    "计算相关系数（矩阵）：\r\n",
    "+ `object.corr()`：\r\n",
    "+ `numpy.corrcoef(data, rowvar=True, ddof=1)`\r\n",
    "+ `dataframe.corrwidth(object, axis=0)`：计算DataFrame的列（axis=0，默认）或行（axis=1时）与另一个Series或Dataframe之间的相关系数"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "# 获取数据\r\n",
    "\r\n",
    "# frame1_1 = pandas.read_csv(\".\\\\data\\\\stoke.txt\", sep=\"\\t\")\r\n",
    "frame1_1 = pandas.read_csv(\".\\\\data\\\\stoke.txt\", delimiter=\"\\t\", index_col=0)\r\n",
    "\r\n",
    "print(frame1_1.dtypes)\r\n",
    "frame1_1.tail()     # 查看末尾n行数据，默认为5行，等价于：frame1_1[-5:]"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "# 计算百分数变化\r\n",
    "\r\n",
    "percent = frame1_1.pct_change()\r\n",
    "percent.tail()"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "# 对两个Series求协方差、相关系数\r\n",
    "\r\n",
    "frame1_1[\"MSFT\"].cov(frame1_1[\"IBM\"])\r\n",
    "frame1_1.MSFT.cov(frame1_1.IBM)        # 也可以这样引用\r\n",
    "\r\n",
    "frame1_1[\"MSFT\"].corr(frame1_1[\"IBM\"])\r\n",
    "frame1_1.MSFT.corr(frame1_1.IBM)        # 也可以这样引用"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "# 对DataFrame求协方差、相关系数\r\n",
    "\r\n",
    "frame1_1.cov()\r\n",
    "frame1_1.corr()"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "# corrwith() 方法\r\n",
    "\r\n",
    "arr_info([ percent.corrwith(frame1_1[\"IBM\"]) ])\r\n",
    "arr_info([ percent.corrwith(frame1_1) ])"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "### 5.3.2 唯一值、值计数以及成员资格 Unique Values, Value Counts, and Membership\r\n",
    "\r\n",
    "+ `Series.unique()`：计算Series中（DataFrame没有此方法）的唯一值数组，按照发现的顺序返回；\r\n",
    "+ `object.value_counts(sort=True)`：值计数，即频数统计。sort参数表示是否按频数大小排序（降序），默认为True；\r\n",
    "+ `pandas.value_counts(object, sort=True)`：对应的pandas函数；\r\n",
    "+ `object.isin(list)`：返回一个布尔数组，表示传入的list中的值是否包含在该数据对象中；"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "# 唯一化：unique()\r\n",
    "\r\n",
    "ser2_1 = pandas.Series([\"b\", \"d\", \"a\", \"a\", \"a\", \"c\", \"b\", \"c\", \"c\"])\r\n",
    "\r\n",
    "arr_info([ ser2_1 ])\r\n",
    "arr_info([ ser2_1.unique() ])\r\n",
    "\r\n",
    "unique_value = ser2_1.unique()\r\n",
    "unique_value_sort = unique_value.sort()     # 直接调用无效：ser2_1.unique().sort()\r\n",
    "arr_info([ unique_value_sort ])"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "# 值计数：value_counts()\r\n",
    "\r\n",
    "arr_info([ ser2_1.value_counts() ])              # 默认按频数大小降序排列\r\n",
    "arr_info([ ser2_1.value_counts(sort=False) ])    # 按定义时出现顺序排列\r\n",
    "\r\n",
    "arr_info([ pandas.value_counts(ser2_1, sort=False) ])   # 对应的pandas函数"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "source": [
    "# 实例：柱状图数据的计算\r\n",
    "\r\n",
    "frame2_1 = pandas.DataFrame({\"data_A\": [1,3,4,6,4,6,3,4,5], \"data_B\": [2,3,1,2,3,5,4,2,5], \"data_C\": [2,5,10,4,5,6,5,6,7]})\r\n",
    "arr_info([frame2_1])\r\n",
    "\r\n",
    "freq_num = frame2_1.apply(pandas.value_counts).fillna(0).convert_dtypes(int)\r\n",
    "arr_info([freq_num])\r\n",
    "\r\n",
    "matplotlib.pyplot.bar(freq_num.index, freq_num[\"data_C\"])"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "【1】\n",
      " 类 型: <class 'pandas.core.frame.DataFrame'>\n",
      "   data_A  data_B  data_C\n",
      "0       1       2       2\n",
      "1       3       3       5\n",
      "2       4       1      10\n",
      "3       6       2       4\n",
      "4       4       3       5\n",
      "5       6       5       6\n",
      "6       3       4       5\n",
      "7       4       2       6\n",
      "8       5       5       7\n",
      "【1】\n",
      " 类 型: <class 'pandas.core.frame.DataFrame'>\n",
      "    data_A  data_B  data_C\n",
      "1        1       1       0\n",
      "2        0       3       1\n",
      "3        2       2       0\n",
      "4        3       1       1\n",
      "5        1       2       3\n",
      "6        2       0       2\n",
      "7        0       0       1\n",
      "10       0       0       1\n"
     ]
    },
    {
     "output_type": "execute_result",
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     "execution_count": 61
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     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "# 成员资格：isin()\r\n",
    "\r\n",
    "selection = ser2_1.isin([\"b\", \"c\"])\r\n",
    "arr_info([ ser2_1, selection ])\r\n",
    "ser2_1[selection]"
   ],
   "outputs": [],
   "metadata": {}
  }
 ],
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